game theory – Pertinent Observations

Pirate organisations

It’s over 20 years now since I took a “core elective” (yeah, the contradiction!) in IIT on “design and analysis of algorithms”. It was a stellar course, full of highly interesting assignments and quotable quotes. The highlight of the course was a “2 pm onwards” mid term examination, where we could take as much time as we wanted.

Anyway, the relevance of that course to this discussion is one of the problems in our first assignment. It was a puzzle .

It has to do with a large number of pirates who have chanced upon a number of gold coins. There is a strict rank ordering of pirates from most to least powerful (1 to N, with 1 being the most powerful). The problem is about how to distribute the coins among the pirates.

Pirate 1 proposes a split. If at least half the pirates (including himself) vote in favour of the split, the split is accepted and everyone goes home. If (strictly) more than half vote against the split, the pirate is thrown overboard and Pirate 2 proposes a split. This goes on until the split has been accepted. Assuming all the pirates are perfectly rational, how would you split the coins if you were Pirate 1? There is a Wikipedia page on it.

I won’t go into the logic here, but the winning play for Pirate 1 is to give 1 coin to each of the other odd numbered pirates, and keep the rest for himself. If he fails to do so and gets thrown overboard, the optimal solution for Pirate 2 is to give 1 coin to each of the other even numbered pirates, and keep the rest for himself.

So basically you see that this kind of a game structure implies that all odd numbered pirates form a coalition, and all the even numbered pirates form another. It’s like if you were to paint all pirates in one coalition black, you would get a perfectly striped structure.

Now, this kind of a “alternating coalition” can sometimes occur in corporate settings as well. Let us stick to just one path in the org chart, down to the lowest level of employee (so no “uncles” (in a tree sense) in the mix).

Let’s say you are having trouble with your boss and are unable to prevail upon her for some reason. Getting the support of your peers is futile in this effort. So what do you do? You go to your boss’s boss and try to get that person onside, and together you can take on your boss. This can occasionally be winning.

Similarly, let us say you seek to undermine (in the literal sense) one of your underlings who is being troublesome. What do you do? You ally with one of their underlings, to try and prevail upon your underling. Let’s say your boss and your underling have thought similarly to you – they will then ally to try and take you down.

Now see what this looks like – your boss’s boss, you and your underling’s underling are broadly allied. Your boss and your underling (and maybe your underling’s underling’s underling) are broadly allied. So it is like the pirate problem yet again, with people alternate in the hierarchy allying with each other!

Then again, in organisations, alliances and rivalries are never permanent. For each piece of work that you seek to achieve, you do what it takes and ally with the necessary people to finish it. And so, in the broad scheme of all alliances that happen, this “pirate structure” is pretty rare. And so it hasn’t been studied well enough.

PS: I was wondering recently why people don’t offer training programs in “corporate game theory”. The problem, I guess, is that no HR or L&D person will sponsor it – there is no point in having everyone in your org being trained in the same kind of game theory – they will nullify each other and the training will do down the drain.

I suppose this is why you have leadership coaches – who are hired by individual employees to navigate the corporate games.

IPOs and right to match

Long time readers of the blog might know that I’m not a big fan of the IPO pop. I’ve traditionally belonged to the party (led by Bill Gurley) that says that a big IPO pop is akin to “leaving money on the table” for the company.

And so as my party has grown, the IPO process itself has also changed. Way back in 2004, Google allocated shares using a simple Dutch auction. Facebook pushed its bankers hard enough on the IPO price that the IPO “pop” in that case was negative. Spotify and Slack and a few other companies went public in a direct listing. Nowadays you have SPACs. It’s all very interesting stuff for anyone interested in market design.

Over the last few years, though, Matt Levine has been trying hard (and sort of succeeding), in getting to move me to the side that says IPO pops are okay. His first compelling argument was the demand-supply (and market depth) one – in an IPO there is a large offload of shares, and so an IPO buyer can expect to get a discount on the shares. Another is that since the IPO is the first time the stock will be traded, buyers in the IPO are taking risk, and need to be compensated for it in the form of a lower price. Fair enough again.

Matt has outdone himself in his latest newsletter on the topic, where he talks about the IPOs of Roblox and Coupang. About Roblox, he wrote:

I mean, I’ll tell you the answer[1]: Roblox sold stock to venture capitalists at $45, and then it traded up in public markets to $70. In a traditional initial public offering, a company sells stock to mutual funds at $45, and then it trades up in public markets to $70. Venture capitalists are not happy when mutual funds get underpriced stock: It dilutes existing shareholders and “leaves money on the table.” Venture capitalists are of course perfectly happy when venture capitalists get underpriced stock; that’s the business they are in.

This served the purpose of moving me more to his side.

This blogpost, however, is about the Coupang IPO.

All normal enough. But here’s the unusual thing about Coupang. Apparently, of the hundreds of investors who put in orders to buy shares in the IPO—many of whom did roadshow meetings and put in work to understand the company and come up with a price—fewer than 100 were allocated any shares, with most of those shares going to about 25 accounts handpicked by Coupang. Coupang apparently kept tight control over the allocation, choosing its investors itself rather than deferring to its underwriters (led by Goldman Sachs Group Inc.). Now those favored investors—investors favored by Coupang, not investors favored by Goldman—will benefit from the IPO pop. Everyone else, who put in the work and decided they wanted to own Coupang, will have to buy in the aftermarket, from those initial investors, and pay up to do so.

Obviously Coupang has left money on the table, but who cares? Coupang underpriced its IPO, but the beneficiaries of the underpricing are the existing investors that it wanted to benefit.

Basically Coupang announced an IPO at a $27-30 price range. It did a roadshow to gauge investor demand. Demand was strong. And then the price range was upped to $31-34. Demand was strong once again. And then, instead of letting its banker Goldman Sachs price the IPO at 34, and allocate the shares to who Goldman thought would make the best investors, Coupang went to its existing investors and told them “we have a bunch of investors willing to buy our stock at $34. What do you think?”

And the existing investors, finding validation, said “Oh, in that case we can pay $35 for it”. In IPL auction parlance, Coupang’s existing investors basically had a “right to match option”. All the other potential investors were asked, and then the existing investors were “more equal” than the others.

The stock duly popped.

Now, right to match in an IPO might be an interesting structure, but I highly doubt that it will sustain. Basically banks won’t like it. Put yourself in Goldman’s shoes for a moment.

They have done all the hard work of pricing the IPO and taking it to potential clients and doing all the paperwork, and at the end of it, their buy side clients are a mostly pissed of bunch – they’ve again done all the hard work of deciding whether the IPO was worth it and then told that they were cut out of the deal.

The least Goldman’s buy side clients would have wanted is the right to match Coupang’s original investors’ offer ($35). Having done all the hard work, and then being forced to buy the stock (if at all) at the popped price of $49, they will be a totally miffed lot. And they would have conveyed their displeasure to Goldman.

One thing about IPOs is that the companies selling the stock play a one-time game, while the bankers (and IPO investors) play a repeated game, participating in IPOs regularly. And because of this, the incentive structure of IPOs is that bankers tend to favour buy side clients than sell side, and so the big pop. And so bankers will not regularly want to do things that will piss off the buy side, such as offering “right to match” to the selling company’s chosen investors.

So will we see more such IPOs?

My take is that inspired by Coupang, some more companies might insist on a right to match while selling their shares in an IPO. And this right to match will piss off the buy side, who will push back against the bankers and demand a right to match for themselves.

And what happens when both sides (company’s favourite investors and bank’s favourite investors) insist on a mutual right to match? We get an auction of course.

I don’t think anyone will have that much of a problem if IPO share allocation gets resolved by a Dutch auction, like Google did way back in 2004.

More on focal points at reunions

On Friday, just before the IIMB reunion started, I had written about reunions being focal points that help a large number of alumni to coordinate and meet each other at a particular date and venue. What I’d not written about there was the problems that could potentially be caused with the said venue being large.

In this case, the venue was the IIMB campus itself. While all official events, meals and accommodation for outstation attendees had been arranged in a single building (called MDC), the fact that people would explore the campus through the event made the task of coordination rather difficult.

The whole point of a reunion is to meet other people who are attending the event, and so it is important that people are able to find one another easily. And when the venue is a large area without clear lines of sight, finding one another becomes a coordination game.

This is where, once again, Thomas Schelling’s concept of Focal Points comes in. The game is one of coordination – to land up at locations in the venue which maximise the chances of meeting other people. While our class WhatsApp group enabled communication, the fact that people wouldn’t be checking their phones that often during the reunion meant we could assume there was no communication. So when you arrived at the venue, you had to guess where to go to be able to meet people.

Schelling’s theory suggested that we look for the “natural, special or relevant” places, which would be guessed by a large number of people as the place where everyone else would coordinate. In other words, we had to guess what others were thinking, and what others thought other others were thinking. Even within the reunion, focal points had become important! The solution was to search at those specific points that had been special to us back in the day when we were students.

On Saturday morning, I took about ten minutes after entering campus to find batchmates – I had made poor guesses on where people were likely to be. And once I found those two batchmates at that first point, we took a further twenty minutes before we met others – after making a better guess of the focal point. Given that the reunion lasted a bit more than a day, this was a significant amount of time spent in just finding people!

A simpler solution would have been to start with a scheduled event that everyone would attend – the venue and starting time of the event would have defined a very obvious focal point for people to find each other.

And the original schedule had accommodated for this – with a talk by the Director of IIMB scheduled for Saturday morning 10 am. It seemed like a rather natural time for everyone to arrive, find each other and go about the reunion business.

As it happened, revelry on the previous night had continued well into the morning, because of which the talk got postponed. The new starting point was to “meet for lunch around noon”. With people who were staying off-campus, and those arriving only on Saturday arriving as per the original schedule, search costs went up significantly!

PS: This takes nothing away from what was finally an absolutely fantastic reunion. Had a pretty awesome time through the duration of it, and I’m grateful to classmates who came from far away despite their large transaction costs.

Indexing, Communism, Capitalism and Equilibrium

Leading global research and brokerage firm Sanford Bernstein, in a recent analyst report, described Index Funds (which celebrated their 40th birthday yesterday) as being “worse than Marxism“. This comes on the back of some recent research which have accused index funds of fostering “anticompetitive practices“.

According to an article that says that indexing is “capitalism at its best“, Sanford Bernstein’s contention is that indexers “free ride” on the investment and asset allocation decisions made by active investors who spend considerable time, money and effort in analysing the companies in order to pick the best stocks.

Sanford Bernstein, in their report, raise the spectre of all investors abandoning active stock picking and moving towards index funds. In this world, they argue, allocations to different assets will not change (since all funds will converge on a particular allocation), and there will be nobody to perform the function of actually allocating capital to companies that deserve them. This situation, they claim, is “worse than Marxism”.

The point, however, is that as long as there is no regulation that requires everyone to move to index funds, this kind of an equilibrium can never be reached. The simple fact of the matter is that as more and more people move to indexing, the value that can be gained from fairly basic analysis and stock picking will increase. So there will always be a non-negative flow (even if it’s a trickle) in the opposite direction.

In that sense, there is an optimal “mixed strategy” that the universe of investors can play between indexing and active management (depending upon each person’s beliefs and risk preferences). As more and more investors move to indexing, the returns from active management improve, and this “negative feedback” keeps the market in equilibrium!

So in that sense, it doesn’t matter if indexing is capitalist or communist or whateverist. The negative feedback and varying investor preferences means that there will always be takers for both indexing and active management. Whether we are already at equilibrium is another question!

Stephen Curry and mixed strategies

Ever since I learnt recently about the rise of Stephen Curry, and Golden State Warriors’ rise using a three-point strategy, my interest in basketball and the NBA has gone up. I still can’t watch a game – the randomly spaced ad-breaks are too mindfucking for that. But I’ve been reading a lot more about Curry and Golden State Warriors and Joe Lacob of KPCB.

There are two ways in which you can attack in basketball – you can either keep tiki-takaing and drive in to get close to the basket to layup/dunk or you can go for a three-pointer. We can think of each basketball attack as a “game”, where the offensive team decides to go for either the three-point or the tiki-taka, and the defensive team decides how to defend against it.

I won’t bother with drawing the payoff table here, but given research on similar “games” in sports (such as penalty kicks in football), it wouldn’t be hard to guess that the dominant strategy here is the “mixed strategy”, where a team chooses at random whether to tiki-taka or long range.

Over time, this would have led to a certain proportion of the time when the team would have decided to take long shots, and defences would have adapted accordingly (defence against a mixed strategy is also a mixed strategy).

What Curry’s extraordinary three-point shooting skills have done is that they’ve completely changed the payoffs for his team, but significantly increasing the payoff of the three-point strategy. So the Warriors have adapted their strategy accordingly, by going for the three-point game more often than the tiki taka game.

And my sense is that Curry’s shooting statistics are so much better than others’ that the proportion with which the Warriors go with the three-point strategy (as the game theoretic solution suggests) is significantly higher than the proportion with which other teams adopt such a strategy in attack.

Consequently, defences have failed to anticipate this change in the payoff matrix and defend like they do against other teams (whose mixed strategy hasnt changed). In other words, the Warriors’ opponents haven’t been playing the optimal strategy while playing against them. And this is what has led to their unprecedented 73-win NBA season.

With time, other teams are likely to adjust and adapt more optimal strategies. It’ll be interesting to see how the Warriors perform next season!

Admission of errors and bad bank loans

I have a policy that whenever I make a mistake, I admit it. I believe that suppressing an error does more harm than good in the long run, and it is superior to admit it at the time of discovery and correct course rather than keeping things under wraps until the shit hits the fan (a la Nick Leeson, for example).

There is another reason I like to admit to my mistakes – by doing so frequently, I want to send the signal that I’m self-aware and self-critical and aware of what I’ve done wrong. This, I believe, sends a signal that I should be trusted more, since I have a grip on rights and wrongs.

It doesn’t always work that way. There was a company I once worked for, where my responsibilities meant that my errors had an immediate material impact on the company. I don’t know if this (direct material impact) mattered, but my signalling went horribly wrong there.

The powers-that-were came from a prior belief that people would suppress their mistakes as much as they could, and that I was admitting to them only because I couldn’t suppress them further. Their reaction to my constant admission of mistakes (I was writing production code, a bad bad idea given my ADHD) was that if I were admitting to so many mistakes, how many more of my mistakes were yet to be discovered?

In other words, the strategy backfired spectacularly, possibly given the mismatch of our priors, and I later figured I might have done better had I tried suppressing (or quietly fixing) rather than admitting. That, however, hasn’t led to a change in my general strategy on this issue.

I was reminded of this strategy when State Bank of India and Punjab National Bank released their quarterly results last week. Their stocks got hammered on the back of drastically reduced profits on account of higher provisions – an admission that a significantly higher proportion of their loans had gone bad compared to their earlier admissions.

The question that comes to mind is whether the increase in provisioning and admission of bad loans should be taken as a credible signal that these banks are cleaning up their balance sheets (which is a good thing) or whether it only indicates a bigger tip of a bigger iceberg (in which case I’d be paranoid about my deposits).

Not knowing what strategy these banks are playing (though statements from the RBI suggest they’re likely to be cleaning up), I guess we have to wait for results over the next couple of quarters to learn their signals better.

Guarantees in meetings

There are some events/meetings which involve strong network effects. People want to attend such events if and only if a certain number of other people are going to attend it. But then they don’t know before hand as to who else is coming, and hence are not sure whether to accept the invitation. These are events such as school reunions, for example, where if only a few people come, there isn’t much value. And it’s hard to coordinate.

In such events it’s always useful to provide a guarantee. For example, a friend from (B) school was in town last week and expressed an interest in meeting other batchmates in Bangalore. A mail thread was promptly started but until the morning of the event, people remained mostly noncommittal. Not many of us knew this guy particularly well, though he is generally well-liked. So none of us really wanted to land up and be among only one or two people along with this guy.

And then there was a guarantee. One other guy sent a mail saying he’d booked a table at a bar, and this sent a strong signal that this guy was going to be there too. Then there were a couple of other very positive replies and the guarantee having been set, some seven or eight people turned up and the meeting can be called a “success”.

Sometimes when you’re trying to organise an event, it makes sense to get unconditional attendance guarantees from a couple of people before you send out the invite to the wider world. So you tell people that “X and Y” (the early guarantors) are definitely coming, and that will pull in more people, and that can be the trigger in making the event a success! In certain circles, X and Y need to be celebrities. In smaller circles, they can be common men (or women), but people whose guarantees of attendance are generally trusted (i.e. people who don’t have a history of standing up people)!

Another small reunion of my B-school batch happened last month and in the run-up to that I realised another thing about RSVPs – yeses should be public and noes private. One guy took initiative and mailed a bunch of us proposing we meet. I hit reply all on purpose to say that it was a great idea and confirm my attendance. Soon there was another public reply confirming attendance and this snowballed to give us a successful event. There were a few invitees we didn’t hear from, who didn’t attend, and I assume they had replied privately to the invite in the negative.

The problem with events on Facebook is that your RSVP is public irrespective of your reply – so even if you say no, everyone knows you’ve said “no”. And so you think it’s rude to say “no”, and say “yes” just out of politeness, even though you have no intentions of attending.

I’ve attended a few events where the hosts estimated attendance based on a Facebook invite and grossly overestimated attendance – too many people had hit “yes” out of sheer politeness.

So the ideal protocol should be “public yes, private no”. Facebook should consider giving this as an option to event creators so that people reveal their true preferences in the RSVP rather than saying “yes” out of sheer politeness.

In that sense it’s like a Vickery auction whose basic design principle is that people reveal their true willingness to pay and not underbid to avoid the winner’s curse!

Offline marketing of online services

Using snail-mail for marketing is an effective strategy for it grabs more of your attention. But messages need to be more personalised to have effect.

This came in the mail yesterday. If you are an old-timer like me, you will recognise it as an “inland letter card”. The edges are frayed because it had been so long since I’d received one such card that I’ve forgotten how to open them.

You will notice that this inland letter came from Bigbasket, the online grocery shopping firm. At first look, it is bizarre that an e-commerce firm is using snail mail for its marketing. On second thoughts, though, it isn’t that bizarre!

The thing with online modes of communication such as email or SMS is that the cost of sending a message is low, very close to zero. What this leads marketers to do is to bombard you with messages. For example, I bought something from Jabong a couple of weeks back and they’ve since sent me at least an SMS a day. I promptly delete them without reading. On my email, I’ve been unsubscribing wherever possible from promotional lists from which I get messages – for they are too frequent and too “vanilla” (it’s bizarre that even marketers who know much about me refuse to use that information in their communication).

In short, there is too much clutter in online (email/SMS) marketing, and the chances of any promotion really standing out and getting the user’s attention is minuscule.

Sending snail-mail, on the other hand, is expensive. It costs you to buy the paper, print out the letters and then you pay for postage. This means that with the advent of cheaper means of communication, most marketers have moved away from it. What that has done is that you get much lesser snail-mail than you used to a few years ago. Which means that the amount of attention you devote to each snail-mail is actually more!

So with snail-mail being the more expensive form of marketing, it is actually more effective for marketers because it draws your attention! (You can think of it as a multi-player prisoner’s dilemma where the marketer wants to maximise her claim on your attention (relative to her costs), and can do so by either using email or snail-mail. The optimal solution, I believe, is a kind of “mixed strategy” – mostly email, but the odd snail-mail here!)

So an online sales company reaching out to you by snail mail is not that bizarre after all. If only they had customised the mail to put my name on it (not hard to do at all), and made it seem like a personal letter, it would have been even more effective!

There have been two occasions in the last five years when I’ve actually responded to upsell campaigns. One was by Airtel who called and offered me a 3G data plan for almost the same price as what I was then paying for my 2G plan. I had been intending to upgrade and I took it.

The other was by Tata Sky, who sent me a beautifully crafted personalised letter printed on thick A4 paper, indicating I was a “premium subscriber” and asking if I wanted to upgrade to Tata Sky+ HD, and giving me a number of a dedicated call center who I had to call to upgrade. It is likely that had it been email I might have discarded it (or if I were using today’s Inbox, marked it as “Done”). Snail mail drew more attention, and the personalisation made me feel good. And I upgraded.

Methods of Negotiations

There are fundamentally two ways in which you can negotiate a price. You can either bargain or set a fixed price. Bargaining induces temporary transaction costs – you might end up fighting even, as you are trying to negotiate. But in the process you and the counterparty are giving each other complete information of what you are thinking, and at every step in the process, there is some new information that is going into the price. Finally, if you do manage to strike a deal, it will turn out to be one that both of you like (ok I guess that’s a tautology). Even when there is no deal, you know you at least tried.

In a fixed price environment, on the other hand, you need to take into consideration what the other person thinks the price should be. There’s a fair bit of game theory involved and you constantly need to be guessing, about what the other person might be thinking, and probably adjust your price accordingly. There is no information flow during the course of the deal, and that can severely affect the chances of a deal happening. The consequences in terms of mental strain could be enormous in case you are really keen that the deal goes through.

Some people find the fixed price environment romantic. They think it’s romantic that one can think exactly on behalf of the counterparty and offer them a fair deal. What they fail to discount is the amount of thought process and guessing that actually goes in to the process of determining the “fair deal”. What they discount is the disappointment that has occurred in the past when they’ve been offered an unfair deal, and can do nothing about it because the price is fixed. But I guess that’s the deal about romance – you remember all the nice parts and ignore that similar conditions could lead to not-so-nice outcomes.

Bargaining, on the other hand has none of this romance. It involves short-term costs, fights even. But that’s the best way to go about it if you are keen on striking a deal. Unfortunately the romantics think it’s too unromantic (guess it’s because it’s too practical) and think that if you want a high probability of a deal, you should be willing to offer a fixed price. And the fight continues.. Or maybe not – it could even be a “take it or leave it” thing.

Relationships and the Prisoner’s Dilemma Part Deux

Those of you who either follow me on twitter or are my friends on GTalk will know that my earlier post on relationships and the prisoner’s dilemma got linked to from Cheap Talk, the only good Game Theory blog that I’m aware of. After I wrote that post, I had written to Jeffrey Ely and Sandeep Baliga of Cheap Talk, and Jeff decided to respond to my post.

It was an extremely proud moment for me and I spent about half a day just basking in the glory of having been linked from a blog that I follow and like. What made me prouder was the last line in Jeff’s post where he mentioned that my blog post had been part of his dinner conversation. I’m humbled.

So coming to the point of this post. Jeff, in his post, writes:

Some dimensions are easier to contract on. It’s easy to commit to go out only on Tuesday nights. However, text messages are impossible to count and the distortions due to overcompensation on these slippery-slope dimensions may turn out even worse than the original state of affairs.

I argue that it is precisely this kind of agreements that leads to too much engagement. The key, I argue, is to keep things loosely coupled and uncertain; and this, I say, doesn’t apply to only romantic relationships. I argue in favour of principles, as opposed to rules. Wherever the human mind is concerned, it is always better to leave room for uncertainty. Short term volatility decreases the chances of long-term shocks.

So if you contract to date only on Tuesday nights, and on a certain Thursday both of you get a sudden craving for each other. In a rule-based system, you’d have to wait till Tuesday to meet, and that would mean that you’d typically spend the next five days in high engagement, since you wouldn’t want to let go given the craving. There is also the chance that when you finally meet, there has been so much build-up that it leaves you unsettled.

The way to go about this is to not make rules and just make do with some simple principles regarding the engagement, and more importantly to keep things flexible. If you have a “I won’t call you when you’re at work” rule, and there is something you really need to say, this leads to wasted mind space since you’ll be holding this thought in the head till the other person is out of office, and thus give less for other things you need to do in that time.

You might ask me what principles one can use. I don’t know, and there are no rules governing principles. It is entirely to do with the parties involved and what they can agree upon. A simple principle might be “if I don’t reply to your text message it doesn’t mean I don’t love you”. You get the drift, I suppose. And the volatility, too. (ok I’m sorry about that one)

The mechanism design problem for scaling down that Jeff talks about is indeed interesting. His solution makes sense but it assumes the presence of a Trusted Third Party. Even if one were to find one such, and that person understands Binary Search techniques, it might take too much effort to find the level of interaction. I wonder if the solution to scaling down also is the Bilateral Nudge (will talk about this in another post).